Problem: $I(t)$ models the daily solar irradiance, measured in $\dfrac{\text{kWh}}{\text{m}^2\text{-day}}$, on a farm, $t$ days after the summer solstice. Here, $t$ is entered in radians. $I(t) = 1.5\cos\left(\dfrac{2\pi}{365}t\right) + 4.3$ What is the second time after the summer solstice that the solar irradiance is $5.2 \dfrac{\text{kWh}}{\text{m}^2\text{-day}}$ ? Round your final answer to the nearest whole day.
Answer: Converting the problem into mathematical terms $I(t) = 1.5\cos\left({\dfrac{2\pi}{365}}t\right) + 4.3$ has a period of $\dfrac{2\pi}{{\scriptsize\dfrac{2\pi}{365}}}=365$ days. We want to find the second solution to the equation $I(t)=5.2$ within the period $0<t<365$. The answer The equation's two solutions within the desired period (rounded to the nearest whole day) are $54$ and $311$. Therefore, the second time that the solar irradiance hits $5.2 \dfrac{\text{kWh}}{\text{m}^2\text{-day}}$ is $311$ days after the summer solstice.